ECLECTIC SYSTEM OF INDUSTRIAL DRAWING 



ELEMENTS OF 
MECHANICAL DRAWING 



HV 



CHRISTINH SULLIVAN, Vw.X). 




353 



NP:W YORK . CINCINNATI : CHICAT.o 

AMERICAN BOOK (;OMPA^^ 




LIBRARY OF CONGRESS. 



©opmin^ !f 0... 

S]ielf..T.3i'3 

aSerica. 



UNITED STATES OF Al 



ECLECTIC SYSTEM OF INDUSTRIAL DRAWING 



ELEMENTS OF 



MECHANICAL DRAWING 



FOR USE IN THE SCHOOLROOM AND THE WORKSHOP 



BY 

CHRISTINE SULLIVAN, Ph.D. 



NEW YORK .:• CINCINNATI •:• CHICAGO 



AMERICAN BOOK COMPANY l^^^lOy^ 
1893 



A 






Copyright, 1893, by 
AMERICAN BOOK COMPANY 



Ele. Mech. Dr. 



CONTENTS. 



LESSON 



PAGE 



I. Materials Necessary, and How to use Them 5 

II. Definitions 7 

III. Definitions, Continued lo 

IV. Definitions, Concluded . . 12 

V. Geometric Problems 16 

VI. Exercise with Ruler and Compasses 20 

VIl. Exercise with Ruler and Compasses, Continued 21 

VIII. Exercise with Ruler and Compasses, Continued 22 

IX. Exercise with Ruler and Compasses, Concluded 22 

X. Geometric Problems . 24 

XI. Geometric Problems, Concluded 26 

XII. Geometrical Solids unfolded 28 

XIII. Perspective 33 

XIV. Scale 35 

XV. Working Drawings 36 

XVI.' Mechanical Powers 38 

XVII. Geometric Solids. — Plans and Elevations 39 

XVIII. Joints 47 

XIX. Masonry 50 

XX. Mechanical Devices 51 

XXI. Mechanical Devices, Concluded 53 

3 



4 CONTENTS. 

LESSON PAGE 

XXII. Architecture o 56 

XXIII. Architecture, Concluded = , 57 

XXIV. Tracing and Blue Printing 58 

XXV. Machinery 58 

XXVI. Machinery, Coficludcd 60 

XXVII. Wheels 61 

XXVIII. Geometric Construction 65 

XXIX. Color 66 

XXX. Isometric Projection . . 68 



ELEMENTS OF 
MECHANICAL DRAWING. 

LESSON I. 
MATERIALS NECESSARY, AND HOW TO USE THEM. 

1. Drawing Board. — This must be of well-seasoned lumber, have 
a smooth surface, and be not less than i8 by 24 inches. 

2. Paper. — The paper must be smaller than the board, so that it 
will not project over the edges. If the drawing is to remain on the 
board but a short time, it may be fastened down with thumb tacks. 
If it is to be some time on the board, it is advisable to dampen the 
paper with a sponge, and paste the edges to the board, stretching the 
paper equally in all directions from the center. 

3. T Square. — This should be held against the left side of the 
board, and should be used for horizontal lines only. Use a triangle 
(90°) for vertical lines. 

4. Pencils. — These must be of good quality ; the lead sharpened 
to a round point for sketching, and to a flat edge for ruling. 

Note. — If the drawings are to be finished in ink, the penciling must be very 
light. 

5. Ink. — The pupil must never use writing fluid, which rusts and 
destroys the instruments. 

5 



6 ELEMENTS OF MECHANICAL DRAWING, 

Note I. — A small quantity of indigo added to the India ink will prevent the 
lines in the drawing from turning brown. 

Note 2. — To make ink waterproof, drop a piece of bichromate of potassium 
about the size of a bean into the bottle of ink. After using this solution, clean the 
ink foot of the compasses and pen thoroughly. 

6. Dividers. — These are employed when distances are to be accu- 
rately measured. 

7. Protractor. — This instrument is used in measuring and con- 
structing angles. It is semicircular in shape, and the arc is divided 
into 180°. 

8. Horn Center. — It is used to prevent the compass foot from 
enlarging any center. 

9. A Pair of Compasses. — They consist of the body of the com- 
passes and three adjustable parts : the steel for measuring ; the 
pencil leg, used for drawing arcs, circles, etc. ; and the ink leg, 
which is used to repeat the pencil work in ink. 

10. Ruling Pen. — This is used for inking straight lines. 

HINTS IN USING THE COMPASSES. 

{a) In describing a circle keep the ink leg perpendicular to the 
surface of the paper by means of a joint in the ink leg. 

[b) In describing circles do not bear weight on the compasses suffi- 
cient to force the steel point through the paper. 

(r) If many concentric circles or arcs are required, the pupil should 
use a horn center. 

(^) Use compasses with round, not too sharp steel point. 

(^) Hold compasses very loosely between the thumb and fore- 
finger only. 

(/) Allow the instrument to rest with equal weight on all points 
of a curve. 

{g) When lengthening rod is used to describe circles of a long 
radius, the pupil must remember to keep the ink leg bent, and per- 
pendicular to the surface of the paper. 



DEFINITIONS. 7 

{H) Bow pen and pencil and spring bows are used for drawing 
small circles. 

Note i. — Ruling pen and compasses may be supplied with ink by means of a 
camers-hair brush. 

Note 2. — Always test pen and compasses before inking in the drawing. 

Note 3. — Always thoroughly dry and clean inking leg and drawing pen before 
putting away. 



LESSON II. 

DEFINITIONS. 

As almost all forms in machinery are geometrical, and as it is 
necessary for the pupil to have a knowledge of the names of the 
different geometrical forms, and also to know how to construct the 
same, the following definitions must be learned by the class. The 
pupil should draw on paper and on the blackboard all exercises 
illustrating these definitions. 

LINES AND SURFACES. 
Note. — For exercises see p. 24. 

1. A straight line is the shortest distance between two points. 

2. Straight lines are horizontal^ vertical^ and oblique. 



Fig. I. — Horizontal Lines. 



Fig. 2. — Vertical Lines. 



ELEMENTS OF MECHANICAL DRA WING, 





Fig. 



- Oblique Lines. 



3. A curved line is a line that changes its direction at every point, 

4. Curves are regular and irregular. 





Fig. 4. — Regular Curve. 



Fig. 5. — Irregular Curve. 



5. Surface has length and breadth without thickness. 

6. \ plane surface is a flat, even surface. 

7. Parallel lines are lines that will not meet, no matter how far 
produced. They lie in the same plane. 






Fig. 6. — Parallel Lines. 



DEFINITIONS. 



ANGLES. 

8. An angle is the amount of divergence between two lines that 
meet in any plane. 

9. An angle is designated by naming its sides, 
or by naming the vertex only. 

10. There are three kinds of angles. 

11. A right angle is formed by one straight line 
meeting another straight line, making the adjacent 
angles equal. It measures 90° (marked R. A.). 

12. An obtuse angle is greater than a right angle. 

13. An acute angle is less than a right angle. ^*^ Angles^"^ 






Fig, 8. — Obtuse Angles. Fig. 9. — Acute Angles. 

14. A curvilinear angle is formed by two curves. 





Fig. 10. — Curvilinear Angles. 

15. A mixilinear angle is formed by a curve and a straight line. 





Fig. II. — Mixilinear Angles. 



i6. 


\ polygon is a 


17. 


A polygon of 


18. 


A polygon of 


19. 


A polygon of 


20. 


A polygon of 


21. 


A polygon of 


22. 


A polygon of 


23. 


A polygon of 


24. 


A polygon of 



25. A polygon of 



ELEMENTS OF MECHANICAL DRA WING. 

LESSON III. 
DEFINITIONS. — Co7itinued. 



POLYGONS. 

surface bounded by straight lines. 

three sides is called a triangle. 

four sides is called a quadrilateral (Fig. 12). 

five sides is called di pentagon. 

six sides is called a hexagon. 

seven sides is called a heptagon. 

eight sides is called an octagon. 

nine sides is called a nonagon, 

ten sides is called a decagon. 

twelve sides is called a dodecagoji. 




Square. 



Rectangle. 



Rhomboid. 





Rhombus. 



Trapezoid. 
Fig. 12. —Quadrilaterals. 



Trapezium. 



DEFINITIONS, 



II 



26. An equilateral polygon is one whose sides are equal. 

27. An equiangular polygon is one whose angles are equal. 



TRIANGLES. 





Equilateral. 



Right-angled. 





Isosceles. 



Scalene. 



Fig. 13. — Triangles. 



28. An equilateral triangle has all sides equal. 

29. A right-angled triangle is one that has a right angle. 

30. An isosceles triangle has two sides equal. 

31. A scalene triangle has no two sides equal. 

32. An equiangular triangle is called a trigon. 

33. Triangles are sometimes trilaterals. 



TECHNICAL TERMS USED IN GEOMETRY. 

34. K point indicates position without magnitude, as the center of a 
circle or the intersection of two lines (Fig. 14). The point of inter- 
section is where two lines cross (Fig. 15). 





Fig. 15. 



Fig. 16. 



12 ELEMENTS OF MECHAXICAL DRAWING. 

35. A litie has length. It indicates direction (Fig. 16). 

36. A given line is a fixed or known line, the length of which is given. 

37. To produce or prolong a line is to lengthen it in the same straight 
line or direction. 

^^. Lines of construction are the lines used in the solution of a 
problem. 

39. To describe a figure is to draw it on a sheet of paper or any- 
other plane surface. 

40. To set off a distance is to mark on the drawing a 
given distance. 

41. The area of a surface is the space which it contains. 

42. Altitude is a straight line drawn from the vertex of 
any figure perpendicular to its base (Fig. 17). 

43. Equal figures are those having the same area. 

44. A perimeter is the outer boundary of a figure, the sum of all 
the sides. 

45. A periphery is the circumference of a circle, ellipse, or other 
regular curvilinear figure. 

46. To bisect is to divide into two equal parts. 

47. To coincide is to agree in every respect, — position, length, etc. 

48. rs. problem is something proposed which requires solution. 

49. An axiom is a self-evident truth. 

50. A taiigent is a straight line that touches a curve at but one point. 

51. A regular polygon is both equilateral and equiangular. 

52. The diagotial of a polygon is a straight line joining the vertices 
of any two angles not consecutive. 




LESSON IV. 

DEFINITIONS. — Concluded. 
THE CIRCLE. 

53. A circle is a plane figure bounded by a curved line every point 
of which is equally distant from a point within called the center. 



DEFINITIONS. 



13 



Circle 



54. A circumference is the curved line that bounds the circle. 

55. A diameter is a straight line that passes through the center, and 
terminates in the circum- 
ference. 

Note. — A circumference is 
3y times its own diameter. 

56. A radius is a straight 
line that extends from the 
center to the circumference. 

57. An arc is a part of 
the circumference. 

58. A sector is the space 
included between the radii 
and arc. 

59. A chord is a straight 
line connecting the extrem- 
ities of an arc. 

60. A segment is the space included between the chord and its arc. 

61. An angle at the center is measured by an arc at the circumfer- 
ence between the sides of the angle. This 
arc is said to subtend the angle. 

62. An angle whose vertex is in the cir- 
cumference is measured by one half the arc 
which subtends it. 

d^i' A secant is a line which meets the 
circumference of a circle in two points, 
and lies partly within and partly without the circumference (Fig. 19). 




Fig. 18. 




Fig. 



QUESTIONS FOR CLASS EXERCISES. 

It is advisable to have a number of pupils, six or eight, at work at 
the blackboard ; the remainder of the class preparing the exercises 
at their desks. 



14 ELEMEXTS OF MECHANICAL DRAWING, 

Exercises in Drawing Horizofital Li7ies. 

1. Define the term horizofital. 

2. Draw five 3-inch lines one fourth of an inch apart. 

3. Draw four 5-inch lines one eighth of an inch apart. 

4. Draw six 4-inch lines one sixteenth of an inch apart. 

Exercises in Drawing Vertical Li?ies. 

5. Draw f\\t 4-inch lines one eighth of an inch apart. 

6. Draw six 3-inch lines one sixteenth of an inch apart. 

7. Draw three 5-inch lines one fourth of an inch apart. 

Exercises in Drawing Oblique Lines. 

8. Draw five 4-inch lines one eighth of an inch apart. 

9. Draw six 3-inch lines one sixteenth of an inch apart. 

10. Draw four 5-inch lines one fourth of an inch apart. 

Note. — Draw these oblique lines from right to left, and then repeat the exercise 
in the direction of left to right. 

Miscellaneous Exercises. 

11. What is a simple curve? Draw one ; radius, 2 inches. 

12. What is a concave surface? Draw one ; radius, \\ inches. 

13. What is a curvilinear figure ? Illustrate by a drawing. 

14. Make a mixed figure with one curve and a straight line. 

15. Make a mixed figure having one line and two curves. 

16. Make a mixed figure having one curve and two lines. 

17. Place two circles to touch each other, centers on a straight 
line ; radii, i inch and \ of an inch. 

18. Place three tangent circles, centers in a vertical line ; radii, | 
of an inch, | of an inch, and i inch. 

19. What are great arcs ; less arcs? Illustrate by drawing; radius, 
1 inch. 



DEFINITIONS. 15 

20. What does the term segment mean ? Illustrate by drawing 
segments of circles, lines, and spheres. 

21. Make a greater segment ; less segment. 

22. Can you cut more than one greater segment from a circle ? 

23. Place two circles so that the circumference of each passes 
through the center of each ; radii, i inch and \\ inches. The curved 
portion is a doicble segment. 

24. In how many ways can you divide a double segment into two 
equal and similar parts '^. Illustrate. 

25. Divide a double segment into four equal and similar parts. 

26. Make two angles with two lines. 

27. What are adjacent angles ? Illustrate. 

28. What is a perpendicular line } Illustrate. 

29. Can you make three angles with two lines ? Illustrate. 

30. Can you make four angles with two lines .?^ More than four 
angles with two lines } 

31. What is a quadrant ? Illustrate with radius of i^^ inches. 

32. What is a degree of a circle (°) ? 

-^2)' Make a right angle ; an acute angle ; an obtuse angle. 

34. A sector which has an arc greater than a semicircle is said to 
have a reentraitt angle. Illustrate. 

35. Concentric circles have a common center. Illustrate with 
radii of \\ inches and less. 

2)(y. Eccentric circles have in part a common circumference but 
different centers. Illustrate. 

37. Divide a sector into two parts that shall be equal and similar 
to each other. 

'^'^. flow would you determine the ratio a circumference bears 
to its diameter ? 

39. Make three concentric circles, the largest circle being i^ 
inches in diameter. 

40. Make two eccentric circles, largest i:^ inches in diameter. 

41. Describe a circle having a radius of i inch, and draw a tan- 
gent to the same. 



i6 



ELEMENTS OF MECHANICAL DRAWING. 



42. Give an example of a tangent to an arc ; radius of arc, f of 
an inch. 

43. Compare angle at center (j5, Fig. 20) and angle at circum- 
ference {^, Fig. 20) with reference to size. 

44. Are arcs intersected by parallel chords 
equal, or unequal ? Illustrate. 

45. What does the term coincide mean ? 

46. Place two triangles so that one side of one 
may coincide with one side of the other. 

47. Divide an equilateral triangle so that the 
two parts may be equal and similar. 

48. What is a sector? 

49. Make an acute-angled sector ; an obtuse-angled sector. 

50. Make three sectors, each containing 180°, and write in each a 
different and appropriate name ; radii, i^ inches. 

51. What does the t^xvoi periphery va^diXvl Illustrate by drawing 
peripheries of circles, ellipses, and other figures. 




LESSON V. 

GEOMETRIC PROBLEMS. 



Problem i. — To bisect a given line. 

Let AB (Fig. 21) be the given line. 
From A and B as centers, and w^ith a 
radius greater than one half the line, 
describe the arcs i and 2. Connect the 
points of intersection by the line i 2, 
which passes through the point C, the 
center of the line, dividing it into two 
equal parts. 





Fig. 21. 



GEOMETRIC PROBLEMS. 



17 



Problem 2. — To construct an angle equal 
to a given angle. 

Let ABC (Fig. 22) be the given angle. 
Draw the line MP, With J/ as a center, 
and a radius MO equal to BC^ describe 
arcs. Measure the arc CA by a chord, 
and with the same chord lay off an equal 
arc OS^ and draw the line MS^ which 
gives the angle at 2 equal to ABC. 





Problem 3. — To construct a tri- 
angle^ two angles and the included side 
given. 

Let I and 2 (Fig. 23) be the angles, 
and AB the included line. Draw the 
line OM, and on it lay off a distance 
equal to the given line AB, and mark 
it CD. At C and D make angles 
equal to i and 2. Produce the sides 
of the angles until they meet in E. 
CDE is the triangle. 



Problem 4. — To construct a square on 
its diagonal. 

Let AB. (Fig. 24) be the given diagonal. 
Bisect the diagonal AB by CD, and 
mark the center point O. On the line 
CD, with (9 as a center and OA as a 
radius, lay off OM and OS equal to OA. 
Join the points A, S, B, M, which gives 
the required square. 




Fig. 24. 



i8 



ELEMENTS OF MECHANICAL DRA WING, 




Problem ^,— To fiiid the center of a 
given circle. 

Draw any two chords AB and ^C (Fig. 
25). Bisect these chords, and prolong 
the bisecting lines. Where these meet, 
locate the required center. 



Problem 6. — To erect a perpendicular from 
a point without a given line. 

Let AB (Fig. 26) be the given line, and O the 
point. From (9 as a center, with a line extend- 
ing above AB^ describe an arc cutting AB in i 
and 2. With these as centers, describe arcs in- 
tersecting in F. Connect i^ and O^ producing 
the required perpendicular. 



X|>- 




*^^=T^. 




Problem 7. — To construct a hexagon. 

Describe a circle. With the radius of the cir- 
cle as a chord, lay off on the circumference the 
points A^ B, C, D, E, F (Fig. 27). Connect these 
points by straight lines, which construction gives 
the required hexagon. 



Fig. 27. 



GEOMETRIC PROBLEMS. 



19 



Problem 8. — To bisect any an 

Let ABC (Fig. 28) be the required angle. 
With ^5* as a center, and BA as a radius, de- 
scribe the arc AC^ and draw the chord AC. 
Bisect this chord (Prob. i). This line also 
bisects the arc and the angle B at the center. 




Fig. 28. 







Fig. 29. 



Problem 9. — To trisect any^angle. 

Let ABC (Fig. 29) be the "angle. From 
^ as a center, describe an arc EF. With 
the same radius, and i^ as a center, describe 
an arc cutting the arc EF in O. From E as 
a center, and the same radius, describe an 
arc, and locate the point S. Through the 
points O and 6' draw lines from B^ dividing 
the angle as required. 



Problem 10. — To construct a rectangle 
whose sides shall be equal to two given lines. 

Let AB and CD (Fig. 30) be the given 
lines. Draw the straight line EF equal 
to CZ>, and from E draw EH perpendicu- 
lar to EF ^xvA equal to AB. From 7^ and 
ZTas centers, with radii equal to AB and 
CD^ describe arcs, and mark their point 
of intersection M. Draw HM and FM. 
EFHM is the required rectangle. 




20 



ELEMENTS OF MECHANICAL DRA WING. 




Fig. 31. 

LESSON VI. 

EXERCISE WITH RULER AND COMPASSES. 

Exercise i. — Describe a circle (Fig. 31). Divide the circumfer- 
ence into six equal parts. Each chord will be equal in length to the 
radius of the circle. Divide each sixth into four equal parts. Con- 
nect each point with every point in the circumference. 



EXERCISE WITH RULER AND COMPASSES, 



21 



LESSON VII. 

EXERCISE WITH RULER AND COUVA'^^^S. — Continued. 

IpXERCiSE 2. — Draw 144 circles in a one-foot square. The 
square (Fig. 32) is divided into one-inch squares, diagonals are 
drawn, and circles are tangent to each side of the small square. 




2 2 ELEMENTS OF MECHANICAL DRAWING. 

LESSON VIII. 

EXERCISE WITH RULER AND COMPASSES. — C^;//2«2/^^. 

Note. — These exercises are not given in the form of or as problems in geometry, 
but as exercises with ruler and compasses. They should be drawn on six-inch hori- 
zontal lines. 

Exercise 3. — Draw several concentric circles on a horizontal diam- 
eter that shall pass through one end of the diameter (Fig. '^i). A 
line drawn perpendicular to this end will be tangent to all the circles. 




Fig. 33. Fig. 34. Fig. 35. 

Exercise 4. — Divide a circle into any number of parts which shall 
be equal to each other in area and perimeter (Fig. 34). The curves 
in this exercise are all half circles drawn on opposite sides of the line. 

Exercise 5. — Produce a spiral on a horizontal diameter by draw- 
ing half circles on both sides of the diameter (Fig. 35). Those above 
the line have one center, and those below the line another center on 
the same line. 

LESSON IX. 

EXERCISE WITH RULER AND COMPASSES. — C^^/r/wa'^d/. 

Exercise 6. — Draw a three-inch square, ABCD (Fig. 2>^). With 
I as a center, and i C as the first radius, describe half circles an 
eighth of an inch apart. 

NoTK. — Care must be taken not to show joining of curves and vertical lines. 



EXERCISE WITH RULER AND COMPASSES. 



-3 




Fig. 36. 



ELEMENTS OF MECHANICAL DRA WING. 



LESSON X. 
GEOMETRIC PROBLEMS. 

Problem i. — To construct a 7'egular pentagon. 

Produce AB to C (Fig. 37), making BC equal to AB. From B as 

a center, with BA as a radius, describe 
the arc ADC, and divide the half cir- 
cumference into five equal parts. From 
the point B draw through the point 2 
the line BD. Bisect BB and BA by 
perpendicular lines meeting in O. From 
(9 as a center, and with OB as a radius, 
describe a circle. From B draw lines ^^ 
and BF through the points 3 and 4 in 
the semicircle. Join the points A, F^ 
E, D, and B^ which gives the required pentagon, ABDEF. 




Problem 2. — In a given squaj-e to inscribe a 
regular octagon. 

Let ABCD (Fig. '^'S) be the given square. 
Draw the diagonals intersecting in the point 
E. From the corners of the square ABCD as 
centers, with a radius equal to AE^ describe 
arcs cutting the sides of the square in the 
points MG, FI, HL, and KN. Join these 
points, and the required octagon will be com- 
pleted. 




Fig. 38. 



Problem 3. — To divide a circle into three concentric parts bearing the 
proportions of i, 2, T) f^om the center. 

Let ABC (Fig. 39) be the given circle. Mark the center Z>, and 



GEOMETRIC PROBLEMS. 



25 



draw AD^ and in this radius describe a semi- 
circle. Divide the radius AD into six equal 
parts. From 4 and 6 draw perpendiculars 
meeting the semicircle in E and F. From D 
as a center, and DE and DF as radii, describe 
the circles which will divide the first circle 
into three parts. 




Problem 4. — To divide a circle into any number of equal or propor- 
tional parts by conccfitric divisio7ts. 

Let ABC (Fig. 40) be the circle to be divided 
into three parts. Draw the radius AD^ and 
divide it into as many equal parts as the circle 
is to be divided into. Upon the radius describe 
a semicircle, and erect vertical lines from the 
points dividing the radius, locating the points 
I and 2. From Z> as a center, and D\ and D2 




Fig. 40. 



as radii, describe circles dividing the first circle 



into three parts. 



Problem 5. — To draiu a straight line equal to any given arc of a 
circle. 

Let AB (Fig. 41) be the given 
arc. Find the center of the arc, 
O^ and complete the circle ABC. 
Draw the diameter BOD^ and pro- 
duce it to J/", making DM equal 
CD. Draw a tangent at B. Draw 
a line from M to A^ and produce 
it to meet. the tangent B in the 
point X, This will give BX equal 
(nearly) to the arc AB. Fk-,. 41. 




Note. — There is no exact method of working this problem. 



26 



ELEMENTS OE MECHANICAL DRA WING. 



LESSON XL 

GEOMETRIC PROBLEMS. — Concluded. 




Problem 6. — To construct a squai-e luhich 
shall be equal to a given circle. 

Describe the circle, and draw the diameters 
at right angles to each other. Through the 
point D (Fig. 42) draw the line MDP tan- 
gent, and equal to the diameter AB. Draw 
the lines CJ/ and 67^, cutting the circumfer- 
ence in S and X. Bisect SM and XP^ and 
join the points i and 2. On this line con- 
struct the square, which will be equal to the 
o^iven circle. 



Problem 7. — To locate the axes of a given ellipse. 

Draw AB and CD (Fig. 43) across the given ellipse, parallel to 
each other. Bisect each of these lines in E and F. Join E and 
F^ and continue until line meets 
ellipse in G and H. Bisect the 
line GH., and from the center O 
draw an arc cutting the ellipse in 
C and M. Draw the line CM. 
Through O draw PS parallel to 
CM, Draw TW 2X right angles 
to PS through the point O. PS 
is the conjugate axis, and TJV tht 
transverse. 




GEOMETRIC PROBLEMS. 



27 



Problem 8. — To construct an egg-shaped oval. 

Draw the diameter AB (Fig. 44). Describe 
the circle AOBM. Draw the radius CO at 
right angles to AB^ meeting the circumference 
in the point O, Join AO and BO^ and produce 
them indefinitely beyond O. With A and B as 
centers, and AB as a radius, describe the arcs 
AD and BE^ terminated by the straight lines 
AE and BD in the points D and E. With 6> 
as a center, and OD as a radius, describe the 
arc DXE, AMBEXD is the required oval. 

Problem 





9. — To draw tan- 
gents to an ellipse from a given 
point without the curve. 

Let A (Fig. 45) be the given 
point. From ^ as a center, with 
a radius equal to its distance 
from F\ the nearest focus, de- 
scribe an arc. From the other 
focus, 7^, with the transverse axis 
BC as a radius, cut the arc in P 
and S^ and join FF and SF^ cut- 
ting the curve in O and M. From 
A^ through these points O and 
My draw the tangents. 



Fig. 45. 

Problem 10. — To draw a tan- 
gent to an ellipse through a given 
point in the curve. 

Let A (Fig. 46) be the given 
point. Find the foci of the 
ellipse FF^ by describing arcs 
with a radius equal to BO with 
Z> as a center, and mark the 




28 ELEMENTS OF MECHANICAL DRA WING. 

points F and F' . From the given point A^ draw straight lines to the 
foci 7^ and 7^', and produce 7^^ beyond the curve to the point J/. 
Bisect the angle MAF\ This bisecting line is the required tangent. 



LESSON XII. 
GEOMETRICAL SOLIDS UNFOLDED. 

The pupil will draw the following geometrical solids (Exercise i), 
and the same unfolded (Exercise 2). He will also draw Exercise 2 
on cardboard, and cut through the outlines. This will give a dia- 
gram whose outline will coincide with the outline of Exercise 2. Cut 
the other lines half through. Fold up the parts and glue the edges, 
and the desired outlines will be formed. 

The object of this lesson is to give the pupil a series of exercises 
that will enable him to understand working drawings clearly and 
thoroughly. To do this he must be able (i) to read a working 
drawing, (2) to make a working drawing, (3) to make the model 
from the working drawing. 

I. ALL FACES EQUAL. 

I. A regular tetrahedron, or equilateral pyramid, is a solid bounded 
by four equal triangles (Fig. 47). 





Exercise i. Exercise 2. 

Fig. 47. 

2. A regular hexahedron, or cube, is a solid bounded by six equal 
squares (Fig. 48). 



GEOMETRICAL SOLIDS UNFOLDED, 



29 




Exercise i. 



Fig. 48. 



Exercise 2. 



3. A regular octahedron is a solid bounded by eight equal triangles 
(Fig. 49)- 




Fig. 49. 



Exercise i. 




4. A regular dodecahedron is a solid bounded by twelve equal 
pentagons (Fig. 50). 




Exercise i. 




Fig. 50. 



30 



ELEMENTS OF MECHANICAL DRAWING, 



5. A regular icosahedron is a solid bounded by twenty equal tri- 
angles (Fig. 51). 





Exercise 1. 



Exercise 2. 



Fig. 51 



11. FACES NOT ALL EQUAL. 

6. A prismhdi^ three or more longitudinal faces and parallel edges, 
and is terminated by two parallel planes of equal size and shape. 

7. A pyramid has three or more faces radiating from a common 
point called a vertex : they inclose a regular polygon, which is called 
the base. 

8. A triangular prism has an equilateral triangle for a base (Fig. 

52). 




Exercise i. 




Exercise 2. 



Fig. 52. 



GEOMETRICAL SOLIDS UNFOLDED. 31 

9. A triangular pyramid \id.^ a three-sided base (Fig. 53). 





Fig. 53. 



10. A quadrangular prism has a square for a base (Fig. 54). 



Exercise i. 



Exercise 2. 



Fig. 



32 ELEMENTS OF MECHANICAL DRAWING. 

II. A quadrangular pyramid \\2.'^ a square for a base (Fig. 55). 




Exercise i. 




Fig. 55- 



12. An hexagonal pris77i has a hexagon for a base (Fig. 56). 



Exercise i. 




Exercise 2. 



Fig. 56. 



PERSPECTIVE. 



ZZ 




Exercise i. 




Fig. 57. 



13. An hexagonal pyramid has a six-sided polygon for a base 
(Fig. 57). 



LESSON XIII. 



PERSPECTIVE. 



A FAIR knowledge of perspective is of the utmost importance to 
the draughtsman. The knowledge and power gained by drawing the 
geometric type forms will enable him to delineate objects that are 
more complicated in construction. He is advised to select these 
rigid forms for models, in order to acquire a knowledge of forms, and 
a power of delineation, that are so necessary. The production of 
pictures will avail little to the pupil studying to become a draughts- 
man, because he will permit little inaccuracies to escape uncorrected 
that can be readily detected in a drawing from a cube, cone, prism, 
or other forms with exact outlines. 

The differences between perspective and projection are, that per- 
spective represents an object as it appears to the eye, and but one 
drawing is required to give a representation of it ; while in a projec- 
tion we have the object represented as it />, and at least two draw- 
ings are necessary to give a complete idea of it. 
3 



34 ELEMENTS OF MECHANICAL DRAWING. 

SUGGESTIONS. 

1. A cube is the type form for rectilinear objects. 

2. A cylinder is the type form for curvilinear objects. 

3. Appearances of objects depend on two conditions, — distance 
and position. Distance produces perspective ; position, fore-shorten- 
ing. 

4. Rectilinear objects in parallel perspective have one face repre- 
sented by an actual drawing, and one vanishing point. 

5. In ajigular perspective no face is represented by an actual 
view, and there are two vanishing points. 

6. The circle, w^hen in full view, is represented by a circle ; when 
viewed obliquely, by an ellipse ; and when viewed edgewise, by a line. 

7. The point of station where the observer stands is the base of an 
upright plane, which the observer is supposed to occupy. All objects 
below his eye are said to be below the level of the eye ; all above, 
above the level of the eye. 

8. Vertical lines are always represented by vertical lines. 

9. Horizontal lines or edges are represented by horizontal and 
oblique lines, — by horizontal lines when the edges are parallel to 
the plane of the observer ; by oblique lines when the edges make 
an angle with this plane. 

10. Retreating lines above the eye seem to run down to a point on 
a level with the eye, and opposite to it ; those below the eye seem to 
run up to the same point. 

11. The apparent width of foreshortened surface may be ascer- 
tained by pencil measuring in space, and the drawing tested by 
rules of perspective. 

12. Lines that are at an angle to the observer, and parallel in the 
object, vanish to one point in the drawing. 

Exercise for Practice. — Make perspective sketches of cube, 
prisms, cylinder, cone, and pyramids. 

Note i. — "Make three drawings of each object : first view, directly in front of the 
observer ; second view, to the left ; and third view, to the right. 

Note 2. — See " Elements of Perspective for Schoolroom and Workshop." 



SCALE. 35 

LESSON XIV„ 
SCALE. 

As objects to be manufactured are generally so large that it is not 
convenient to draw them the actual size, they are represented by 
drawings many times smaller. 

The proportions between these objects and the drawings are called 
scales. If the object is ten feet high, and the drawing is made ten 
inches high, the scale is one inch to the foot (i" to i') ; if this same 
object is represented by a drawing twenty inches high, the scale is 
two inches to the foot ; if by a drawing only five inches high, half an 
inch to the foot ; if by a two-and-a-half-inch drawing, a quarter of 
an inch to the foot. This last, a quarter of an inch to the foot, is 
the scale most commonly used by draughtsmen. 

In making drawings, the pupil works first from measurements from 
plates and models, reducing or enlarging as directed. 

This practice gives facility in copying ready-made drawings, and is 
indispensable in the first lessons. 

Later the pupil will take rough sketches, using the pencil and 
two-foot rule only. A rough sketch of the object is made, and 
accurate measurements of every part jotted down. From these 
drawings and figures the mechanical drawings are made by means 
of the instruments. All lines and parts are drawn according to the 
accepted scale. 

EXERCISES FOR PRACTICE. 

Exercise i. — Draw a line 8' high, scale ^" to i'. 

Exercise 2. — Draw a rectangle 9' by 4', scale ^' to i'. 

Exercise 3. — Draw a 10' square, scale -g-'' to i'. 

Exercise 4. — Draw a circle, diameter 15', scale f" to i'. 

Exercise 5. — Measure with two-foot rule, and represent with 
lines the following : front line of platform, side wall of room, rear 
wall of room, horizontal length of window sill, height and width of 
door. Use the following scales for each measurement : ^\ f", ^". 



36 ELEMENTS OF MECHANICAL DRAWING, 

LESSON XV. 
WORKING DRAWINGS. 

A wo7'king drawing of any object is one that gives the shape of 
the parts. The sizes of the different parts are indicated by figures. 
Perspective represents the objects as they appea?\ 

Working drawings, or projections, represent the objects as they 
are. Fig. 48, p. 29, shows perspective and working drawings of a cube. 

In making working drawings, certain lines and conventions or 

signs are made 
use of. These 

^ are: i. Full or 

_^ d visible line 

Fig. 58. (^)' 3. Work- 

ing line {c)\ 4. 
Invisible line {d)\ 5. Half tint {e) \ 6. Figuring {^' = ^ feet, 10" 
= 10 inches). 

1. Full or visible lines are continuous lines that represent visible 
edges or profiles. 

2. Center lines represent no part of a drawing. They are vertical 
lines of indefinite length. They indicate where the middle of the 
working drawing will fall on the paper. 

3. Working lines are used to carry one point or distance to another. 

4. I7ivisible lines are those which represent invisible edges or 
profiles. 

On working drawings, feet and inches are marked thus : feet, ' ; 
inches, ". Arrow lines are made in connection with the figures indi- 
cating proportions or sizes. These lines are called dimension li?ies. 

Working drawings are not made freehand, but with instruments, 
and are often called instrumental drawi?igs. 



WORKING DRAWINGS. 



37 



EXERCISES FOR PRACTICE. 

Exercise i. — Make several drawings (Fig. 59), using dimensions 




Exercise i. 



Exercise 2. 





-^ ^ 


\ 


k'eV 


< 3'0" > 


<l'6'> 
> 


-. ^ 


/ 









C 0" 
Exercise 3. 




Fig. 59. 



Exercise 4. 



of your own selection, introducing all the lines explained in this 
lesson. 

Exercise 2. — Write out an explanation of each exercise, and make 
perspective sketches after the following suggestion : " Exercise i, 
Fig. 59, shows working drawings of a box, 7^' high, 16' long, and 4' 
wide." 



38 ELEMENTS OF MECHANICAL DRAWING. 

LESSON XVI. 

MECHANICAL POWERS. 

All machines and mechanical devices, numerous and varied as 
they are, are combinations of the six simple mechanical powers : 

1. Lever; 2. Pulley: 3. Inclined plane; 4. Wedge; 5. Screw; 6. 
Wheel and axle. 

1. A lever is an inflexible bar that can be moved about a fulcrum ; 
as, a crowbar, steelyard, balance, hand-truck, poker, scissors, pincers, 
nutcracker, tongs, door on hinges, etc. 

Note. — The nearer the fulcrum is to the weight, the greater the power gained. 
The pupil will make drawings illustrating the definition. 

2. N pulley is a w^heel with a grooved circumference, over which a 
rope passes. It is fixed to the frame by means of an axis on w^hich 
the wheel turns. 

Note. — Pulleys are used to change the direction of motion. Illustrate. 

3. An inclined plane is a plane at an angle to the ground plane. 

Note. — It is used to facilitate motion or movement over an uneven surface. 
Illustrate. 

4. Wedges are of two kinds : r. Those having one inclined surface ; 

2. Those having two inclined surfaces. 

Note — The first class are used for raising weights ; the second class, for splitting 
wood timbers, rending rocks, etc. Illustrate. 

5. A screw consists of a cylinder with threads wrapped around it. 
The hollow cylinder, grooved on the inside, that receives this, is 
called a 7iut. 

Note. — Screws are used when continued pressure is required in a small space. 
Illustrate. 

6. A wheel and axle is a lever of the first kind, giving uninter- 
rupted motion. It is called the endless lever, capstan and windlass^ etc 
Illustrate. 



GEOMETRIC SOLIDS, — PLANS AND ELEVATIONS, 



39 



LESSON XVII. 



GEOMETRIC SOLIDS. — PLANS AND ELEVATIONS. 

All objects have three dimensions, — length, breadth, and thickness. 

Perspective is the art of representing them as they appear. 

Projection is the representation as they exist or really are. 

Projections dire also termed constructive or working drawings. They 
represent the real forms of objects and their dimensions according 
to a given scale. They represent plans and elevations, and are used 




Fig. 6o. 



by machinists, architects, builders, and inventors. In making pro- 
jections, the outlines of the object and its parts are supposed to be 
projected, or thrown on a vertical and on a horizontal plane. These 
planes or surfaces are at right angles to each other, like the floor 
and the wall of a room. The floor is termed the Jiorizontal plane, 
and the wall the vertical plane. When the object is located, and its 
vertical features projected on the vertical plane, we have the vertical 
projection^ or elevation. When the horizontal features are projected 
on the horizontal plane, we have the Jiorizontal projection, or the plan. 



40 



ELEMENTS OF MECHANICAL DRA WING, 



EXERCISES FOR PRACTICE. 




Fig. 6i. 

tions (scales, i" to i', and ■^" to i). 

Note 2. — In blackboard drawings allow 3 inches to 
each inch actual measurement. 

Exercise 3. — Draw a cylinder 6 feet high, 
diameter of base 
being 4 feet (Fig. 
62) ; also plan 
and elevation 
(Fig. 63). 



Exercise 
I. — Draw plan 
and elevation 
of a square 
(Fig. 60). 

Exercise 
2. — Draw plan, 
elevations, and 
perspective of 
a cubical box 
(Fig. 61). 

Note i. — The 
pupil will draw on 
blackboard and on 
paper the geomet- 
rical solids and 
their vertical and 
horizontal projec- 




FiG. 6: 



tlG. t3. 



GEOMETRIC SOLIDS, —PLANS AND ELEVATIONS. 



41 



Exercise 4. — Draw a cone 4 feet high, diameter of base 4 feet 
(Fig. 64) ; also plan and elevation (Fig. 65). 




Fig 64. 
Ppojec-bions, 





Fig. 65. 




Fig. 66. Fig. 67. 

Exercise 5. — Draw a sphere having diameter of 6 feet (Fig. 67) ; 



also plan and elevation (Fig. 66). 



42 



ELEMENTS OF MECHANICAL DRAWING. 




Fig. 68. 



Projections. 



Front Elevation 




Side Elevation 




Fig. 69. 



Exercise 6. — Draw a box 10 feet long, 5 feet high, and 4 feet 
wide (Fig. 68) ; also plan and elevations (Fig. 69). 



GEOMETRIC SOLIDS,— PLANS AND ELEVATIONS, 43 




Exercise 7. — Draw a pyramid 8 feet high, 
having a base 5 feet square (Fig. 70) ; also plan 
and elevations (Fig. 71). 



44 



ELEMENTS OF MECHANICAL DRA WING. 



Exercise 8. — Draw a trun- 
cated cone 7 feet high, diame- 
ter of base 8 feet, diameter of 
top 2 feet (Fig. 72) ; also plan 
and elevation (Fig. 73). 




Fig. 72. 



Fig. 73. 



GEOMETRIC SOLIDS.— PLANS AND ELEVATIONS, 45 



Exercise 9. — Draw a hollow cylinder 7 
feet high, diameter 4^ feet, diameter of open- 
ing 2\ feet (Fig. 74) ; also plan and elevation 
(Fig. 75). 





Fig. 74. 



Fig. 75. 



Exercise 10. — Draw a hemisphere with 
diameter of 4 feet (Fig. 76) ; also plan 
and elevation (Fig. 77). 





Fig. 76. 



Fig. 77. 



46 



ELEMENTS OF MECHANICAL DRA WING, 



Fig. 78. 




Fig. 79. 



Exercise it. — Draw a cubical box 6 feet each way, opening 3^ 
feet (Fig. 79) ; also plan and elevations (Fig. 78). 



JOINTS. 



Al 



LESSON XVIII. 

JOINTS. 
EXERCISES FOR PRACTICE. 

Exercise i. — Draw a corner joint (Fig. 80). 

Exercise 2. — Draw a notched joint (Fig. 81). 

Exercises 3, 4, and 5. — Draw a mortise and tenon (Figs. ^2^ '^^^ 84). 



Fig. 80. 



1 




Fig. 82. 



48 



ELEMENTS OF MECHANICAL DRA WING, 



Exercise 6. — Draw a joist and flooring (Fig. 85). 
Exercise 7. — Draw a beam and stirrup (Fig. ^6^. 

Note. — The pupil will make sketches of the following, tongue and groove and 
dovetail, from objects, not from drawings, and make working drawings of the same 
to scale. 







'^ 



Fig. 83. 







Fig. 84. 



Fig. 85. 



JOINTS. 



49 




Fig. 86 



ST ^^^^^Nj' 



5° 



ELEMENTS OF MECHANICAL DRAWING, 



[o 



LESSON XIX. 
MASONRY. 

Exercise i. — Stone work (Fig. 87, a). 

Exercise 2. — Stone joint (Fig. 87, b). 

Exercises 3 and 4. — Brick footings (Fig. 87, Cy d). 

Exercise 5. — Draw plan and elevations of a chimney (Fig. 87, e) 



g«i„w„„,^ ;;;«iiiiii!iwj ^»-..!"t. 






'•'In.'"""^'' 



«>"i! 



'"""yiii|i!!ii!!l"';. 



'"%f- ■'iijiii'f' 



'^ •"""■• feii..""%h 



r,l|l""'-'l„!.'W' 



•1... "'4& 



■(/|l'"' ■..'., 'lilll 



•"»wf| ■■. yi'-' 




Stone Work 



Stone Joint 



1 , I 



J-ZL 



TIL 



rzL 



I I I 



HI 



Ezr 



^i 



1 , 1 .1 



i , 1 , 1 



^^5" 



I . 1 . 1 ,1 



I , I , I , I 



-^=1=^?=?^ 



• Brick Footin 



1 




Side View 



Plan 



w 



Fig. 87. 



^ 



MECHANICAL DEVICES, 



51 



Exercise i. 
(Fig. %Z), 



LESSON XX. 
MECHANICAL DEVICES. 

Elevation and plan of hexagonal nut and washer 



Elevation. 




Fig. 88. 



52 



ELEMENTS OF MECHANICAL DRAWING, 




Side Elevation 



End Elevation 



Fig. 89. 



Exercise 2. — Side and end elevation of screw punch (Fig. 89). 



Note. — Pupils will make sketches of faucet., wrench, and pulley, and from these 
sketches make working drawings to scales. 



MECHANICAL DEVICES, 



53 



LESSON XXI. 

MECHANICAL DEVICES. — Concluded, 

Exercise 3. — Screw chuck, full size (Figs. 90, 91). 

Note.-— The pupil will make sketches of the washer, bolt and nut, coupling, and 
rivets, and from these sketches make working drawings to scales. 



Side Elevation 
of Screw Chuck 




Fig. 90. 



54 



ELEMENTS OF MECHANICAL DRA WING. 








o 
Q 



MECHANICAL DEVICES. 



55 




Side View. 



Front View. 



Fig. 92. 

Exercise 4. — Lathe carrier (Fig. 92). 



56 



ELEMENTS OF MECHANICAL DRA WING. 



tj- 



ID 

U 



< 



X 

:^ 

o 

in 



B3 






Ba 



T 



"1 
J 



^Dr 






_£ 

--0 




1 







ARCHITECTURE. 



57 



LESSON XXIII 

ARCHITECTURE. — Concluded, 

Exercise 2. — Draw detail of window, interior and exterior ; scale, 
-iV' to i' (Fig. 94). 

Note. — The pupil will take measurements of a door, and make working draw- 
ings of the same (scale, i" to i). 




Interior* 



Exterior 



Fig. 94. 



SS ELEMENTS OF MECHANICAL DRAWING, 

LESSON XXIV. 
TRACING AND BLUE PRINTING. 

After the pupil has made a working drawing in lead pencil, he 
will *' ink in " the same with compasses and ruling pen, and with soft 
rubber or bread erase all traces of pencil and finger marks. He will 
then cut a piece of *' tracing linen " the same size as the paper on 
which he has just finished a drawing, and fasten it on his drawing 
board, croer his finished drawing, with thumb tacks (unglazed side of 
tracing linen up), and trace on it all the lines in the finished drawing. 

When all the lines have been reproduced on the linen, place the 
tracing just made over a similar-sized chemically prepared blue- 
print paper, and place them under a sheet of clear glass on a 
drawing board. Expose this to the direct rays of the sun for four 
minutes. When the sun is not bright, it will be necessary to expose 
the tracing (over the blue-print paper and under the glass) from 
eight to ten minutes. At the end of the time, remove the glass and 
the tracing, and pass the blue-print paper through a large flat pan of 
water until all the lines of the tracing and drawing appear in lines of 
white on a blue ground. Let the water drain off the paper. Put the 
tracings and blue prints away for safe keeping with the drawings. 



LESSON XXV. 
MACHINERY. 

Fig. 95 represents a side elevation of a steam engine (scale 3" 
to i'), showing the steam ports, cylinder, valve box, and other details. 
The pupil will take rough sketches of stationary or locomotive 
engines (out of school hours), and make working drawings or 
draughtings of the different parts and of the whole. 

Note. — The pupil will make rough sketches of the following : cylinder, piston, 
steam ports, valves, crank pin, cotter, connecting roil, motion block, valve rod, 
piston rod, pedestal, plummer block, eccentric, and other details, and, according to 
scale, reproduce them in finished drawings, making tracings and blue prints of same. 



MACHINERY, 



59 







Go 



ELEMENTS OF MECHANICAL BRA WING. 



LESSON XXVI. 

MACHINERY. — Concluded. 

Exercise i. — Draw a piston (Fig. 96). 
Exercise 2. — Draw a crank (Fig. 97). 
Exercise 3. — Draw an eccentric (Fig. 98). 
Exercise 4. — Draw governors (Fig. 99). 



ot 



^\ 



a 



I 



Fig. 96. 




m: 



Fig. 98. 






Fig. 



97- 





Fig. 99. 



WHEELS. 



6i 



Exercise 5. — To produce a given straight line beyond a given ob- 
stacle. 

Let AB (Fig. loo) be the straight line, and X be the obstacle. 




Fig. too. 

Continue a straight line beyond the obstacle. From A and B^ or any 
other points in this line, draw two perpendiculars of equal length, AM 
and ^*S(let them fall beyond the obstacle). Draw MS^ and produce 
it indefinitely. At any two points beyond the obstacle locate H and 
Oy and from these draw the perpendiculars HC and OD^ equal in 
length to AM. Draw the line CZ>, which is the required prolonga- 
tion of AB. 



LESSON XXVIL 
WHEELS. 



In order to transfer motion or force from one axis to another, 
wheels furnished with teeth are employed. 

There are various kinds of wheels, — spur wheels, cog wheels, face 



62 ELEMENTS OF MECHANICAL DRAWING, 

wheels, crown wheels, annular wheels, bevel wheels, miter wheels, 
and skew bevels. 

The curves described, or used for the form of the teeth, are: 
I. The cycloid ; 2. The epicycloid ; 3. The hypocycloid. These curves 
are traced on the following lines : — 

I. The cycloid \s traced by any point in a circle while rolling along 
a straight line (Fig. loi). 




Fig. 101. 

2. The epicycloid is traced by any point in a circle rolling on another 
circumference or arc. 

3. The hypocycloid is traced by any point in a circle rolling on 
the inner side of the circumference. 

Note. — Although these wheels are designed and the patterns for them made on 
scientific principles, still, by considering the curves as portions of circles, they may 
be made sufficiently accurate for general purposes of drawing. 

The cycloid is a curve described by a point in the circumference 
of a circle during one revolution. The line upon which the circle 
rolls is called the director. The circle is called the generating circle, 
and the point in it is called the generator. 

The cycloid was invented by the famous mathematician Galileo 
of Pisa, toward the close of the sixteenth century. 

To trace a cycloid by mechanical means, fasten a straightedge to 
any board. Take a circular piece of wood and fix a small knob in 
the center O (Fig. loi), and cut a small notch in the circumference 



WHEELS. 



63 



M. Roll the disk along the straightedge by means of the knob at 
O, keeping the point of a pencil in the notch at M. The line 
described by the pencil is a cycloid. 

If instead of a straightedge a circle or arc be employed, the curve 
traced by the pencil will be an epicycloid. 

Problem. — To draw a cycloid^ the generating circle being given. 
Let C (Fig. 102) be the center of the generating circle, and AB the 





^^ 




S 


"n 


^^ 










7^ 











5 




/^ 


H 


7 


c 


s 


E 






f 


r. 






\ 






J 






g 


^ / 






M 


V^_ 


y 


D 









o 

Fig. 102. 



W 



director. Divide each half of this circle into four equal parts (each 
half may be divided into any number of equal parts), and through 
each point, Z>, jS, F^ G, H, M^ draw lines indefinitely, parallel to AB. 
Draw the diameter OS^ and from O lay off each way on the line AB 
the same number and sized spaces as we have on the half circle. 
From each of these points, jP, R^ 7", F", W^ X, K, Z, erect perpendicu- 
lars to meet the line i 2. With a radius CO, and a center in the 
next point to the right or left, 7 or 8, describe an arc, cutting the 
third parallel ; from the next point to the right or left as center, and 
the same radius, describe an arc cutting the second parallel ; and so 
on. The points thus located on the parallels are the points on the 
curve through which the cycloid will pass. 



64 



ELEMENTS OF MECHANICAL DRA WING, 



Exercise. — Draw projections of cog wheel 3' in diameter (scale 

r to i'). 



m? ^ 




Fig. 103. 



GEOMETRIC CONSTRUCTION. 



65 



LESSOxN XXVIII. 



GEOMETRIC CONSTRUCTION. 



Exercise i. — In an equilateral triangle inscribe three equal 
circles tangent to each side and to each other (Fig. 104). 

Exercise 2. — In a square inscribe four equal circles tangent to 
each side and to each other (Fig. 105). 

Exercise 3. — In a pentagon inscribe five equal circles tangent to 
each side and to each other (Fig. 106). 

Exercise 4. — In a hexagon inscribe six equal circles tangent to 
each other and to each side of the polygon (Fig. 107). 

Exercises. — In an octagon inscribe eight equal circles tangent 
to each other and to each side (Fig. 108). 




Fig. 





Fig. 106. 





Fig. 108. 



66 



ELEMENTS OF MECHANICAL BRA WEXG, 



LESSON XXIX. 

COLOR. 




A 




Fig. 109.— Borders for Papers. 

It is advisable to color working drawings in order to show at a 
glance the materials of which the different parts are to be made. 

A correct outline drawing is the first requisite, as no amount of 
coloring, no matter how acceptably it may be finished, will improve 
a poor or faulty outline. 



COLOR. 67 

SUGGESTIONS. 

1. Stretch paper as suggested in Lesson I. Never use '' hot- 
pressed " paper. 

2. Fasten a camel's-hair pencil, or brush, at each end of the brush 
handle, — one brush for color, the other for clear water. Caution : 
Do not have too much liquid in the brushes, as it will run on the 
hand or paper. 

3. Select the color to be used on the drawing, and rub one corner 
of it in a small pan or dish, and add water until the paint is ready 
for use. If tube colors are used, screw off the top of the tube and 
squeeze out a very small quantity into the pan. Add water. In 
order that a color should flow easily and cover a surface evenly, it 
should be thin. 

4. When ready to color the drawing, fill the brush with the color 
prepared, and, holding it nearly upright, pass quickly over the upper 
part of the drawing, washing from upper left to lower right as 
rapidly as possible, so that the whole surface may be covered before 
any part dries. 

5. In order to obtain the practice to lay a flat wash of color evenly, 
fill in triangles, squares, circles, etc., with color washes. Color small 
surfaces at first. 

6. Use a large brush in preference to a small one, as a small one 
is likely to streak the wash. In using a large brush, great care must 
be exercised to prevent the color wash from passing over the out- 
lines. 

7. When the color has been washed on, do not touch it until it is 
dry. 

The following substances are generally represented by draughts- 
men as here indicated : — 

1. Brass. — Gamboge or Roman ocher, shaded by sepia. 

2. Brickwork (in elevations). — Lake, mixed with burnt sienna or 

Venetian red. 
Brickwork (in plans and sections). — \^ermilioii and crimson. 



7. Iror 



6S ELEMENTS OF MECHANICAL DRAWING, 

3. Clay or earth. — Vandyke brown or burnt umber. 

4. Concrete work. — Sepia, or neutral tint. 

5. Copper. — Orange. 

6. Granite. — Pale India ink. 
Red granite. — Lake and sepia. 

feast iron (in plan and elevation). — Neutral tint 
J cast iron (in section). — Very light wash of gray 
wrought iron (in plan and elevation). — Indigo, i 
wrought iron (in section). — Indigo, very light, j 

8. Woods. — Pale w^ashes of burnt sienna. 

9. Lead. — Pale indigo, tinged with India ink. 

10. Oak. — Vandyke brown. 

11. Steel. — Pale indigo, tinged with lake. 

12. Stone. — Pale sepia. 

13. Slate. — Indigo and lake, or Payne's gray. 

14. Limestone. — Indigo. 

15. Tin. — Pale Prussian. 



Or Prus- 
sian 
blue. 



LESSON XXX. 
ISOMETRIC PROJECTION. 

Isometric projection differs from perspective and orthographic 
projection, inasmuch as it shows the view of the entire object, and 
all the lines in the drawing may be measured by a uniform scale. 
It is called the perspective of the workshop. This style of represent- 
ing objects was first used by Professor Farish of Cambridge, in 1820. 

In perspective drawings objects diminish in size as they appear 
more distant, according to optical laws, and it is impossible to 
measure their sizes. In orthographic projection two drawings are 
required, and the lengths of the lines are altered according to the 
angle at which the object may be placed. The whole system of 
isometric projection — meaning projections with equal measurements 
— is based on a cube so situated with relation to the horizontal 



ISOMETRIC PROJECTION. 



69 




plane that its projection on the vertical plane will be a hexagon 

BCDHFE (Fig. no). The three visible faces of the cube are equal 

in the representation. The 

angles are not right angles, 

as in the actual cube, but 

are acute and oblique, — 

two acute angles 60°, and 

two oblique angles 120°. 
The line BC leaves the 

horizontal line MO at an 

angle of 30°, making the 

representation of the right 

angle an acute, ABC, 

measuring 60°. The lengths of the lines are established by a scale. 

Vertical lines are represented by vertical lines. The angle at A 

measures 120°. The line AD, and all other lines of the object 

parallel to BC, are made parallel to BC in the representation." The 

faces ABEF and ADHF are drawn in the same manner as the face 

ABCD, 

An isometric drawing unites plan, elevation, and projected view in 

one. 

To construct an 
isometric scale so 
that the object to be 
drawn may be one 
twelfth of the real 
size, proceed as fol- 
lows (as the scale is 
one inch to the foot, 
and as an inch is one 
twelfth of a foot, 
each of the twelfths 




Fig. 



will represent an inch): — 

Draw the line BD (Fig. in) an inch and 



half long, representing 



70 ELEMENTS OF MECHANICAL DRAWING. 

the real length of an object one foot and a half. Mark on BD the 
twelfths of inches which are to represent inches on the scale. 

Make the angle BDM ^o^ , with the set square, and bisect it. This 
gives the angle BDO^ 15°. From the point B draw an angle of 45° 
to DX. From each point marked off on the line draw lines parallel 
to the line BX, The divisions on DX will represent inches, and 
the line DX is an isometrical scale of -^^. Or, instead of making 
a scale, lay off on the lines which will represent the figure when 
completed, in isometric projection, the exact measurements. Thus, 
to draw a cube of 4' o'' in isometric projection, lay off the line AB 
(Fig. no) vertical, 4' o'' long. From the point B project the lines 
BC and BE at angles of 30° each with the base line, measuring 
4' o" along the lines to points C and E. At these points establish 
verticals 4' o" long. Connect the point A with E and D by lines 
parallel to BE and BC. From D and E project lines parallel to 
AE and AD^ until they meet in H, Represent bottom of cube by 
dotted lines from E and C, parallel to EH 3.nd Z^ZT respectively. 

EXERCISES FOR PRACTICE. 

Exercise i. — Draw an isometric view of a cube (Fig. no). 

Exercise 2. — Draw an isometric scale (Fig. in). 

Exercise 3. — Draw plan (Fig. 112) and isometric projection (Fig. 
113) of a flight of steps. 

Exercise 4. — Draw plan (Fig. 114) and isometric projection (Fig. 
115) of dovetailed joint. 

Exercise 5. — Draw plan (Fig. it6) and isometric projection (Fig. 
117) of a summerhouse. 

Exercise 6. — Draw plan (Fig. 118) and front elevation (Fig. 119) 
and isometric projection of a summerhouse. 

Exercise 7. — Draw front elevation and isometric projection 
(Fig. 120) of an arch. 

Note. — The plan of Exercise 5 is here given, and the pupils will make at least 
two elevations of the summerhouse. 



ISOMETRIC PROJECTION. 



n 



Fig. 112. 




Fig. 113. 



7^ 



ELEMENTS OF MECHANICAL DRA WING. 



y'v /' 

m 




— 


--:---,■-.■ ..-! 


— _ 


-^:^^A 


-- — , — ^ 






•■ - ( 



Fig. 114. 




Fig. 115. 



ISOMETRIC PROJECTION. 



73 




Fig, ii6. 



Fig. 117. 



74 





ISOMETRIC PROJECTION. 



75 




